Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
arXiv:2007.02247
Abstract
In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and étale settings for smooth quasi-projective varieties in as broad a context as possible: for example, for varieties over non-separably closed fields in all characteristics, and also for both the étale and motivic settings. In view of the fact that the most promising applications of the traditional Becker-Gottlieb transfer has been to torsors and Borel-style equivariant cohomology theories, we focus our applications to motivic cohomology theories for torsors as well as Borel-style equivariant motivic cohomology theories, both defined with respect to motivic spectra. We obtain several results in this direction, including a stable splitting in generalized motivic cohomology theories. Various further applications will be discussed in forthcoming papers.
This is an updated version where we have made several improvements, for example, the relationship between equivariant and non-equivariant spectra that plays a rather subtle role in the construction of the transfer is discussed in detail. Showing the existence of splittings using the transfer is discussed in a short separate (new) paper that is now also available on the arXiv